ISEE Upper Level Quantitative Reasoning - How to find the length of the diameter

You have a circular lens with a circumference of $16.67 \pi in$ , find the diameter of the lens.

Explanation

You have a circular lens with a circumference of $16.67 \pi in$ , find the diameter of the lens.

Begin with the circumference of a circle formula.

$C=2 \pi r$

Now, we know that

Because our radius is half of our diameter.

So, we can change our original formula to be:

$C= \pi d$

Now, we can see that all we need to do is divide our circumference by pi to get our diameter.

$\frac{C}{\pi}=d$

Now plug in our known and solve:

$\frac{16.67 \pi in}{\pi}=d=16.67 in$

So our answer is 16.67inches

If the value of a radius is $x^{2}-^{\sqrt{x+4}}+2$ , what is the value of the diameter if the value of ?

$22-^{2\sqrt{7}$

$11-^{\sqrt{7}$

$22-^{\sqrt{14}$

$11-^{\sqrt{3}$

Explanation

If the value of a radius is $x^{2}-^{\sqrt{x+4}}+2$ , and the value of , then the radius will be equal to:

$3^{2}-^{\sqrt{3+4}}+2$

$9-^{\sqrt{7}}+2$

$11-^{\sqrt{7}$

Given that the diameter is twice that of the radius, the diameter will be equal to:

$2(11-^{\sqrt{7}})$

This is equal to:

$22-^{2\sqrt{7}$

A series of circles has the following radius values:

If the diameter is then calculated for this set, what would be the median diameter?

Explanation

The median is the middle number in a set when that set is ordered smalles to largest.

When is ordered smallest to largest, we get

Here, the median would be .

Given that a diameter is twice the radius, the diamater would be (twice the value of ).

The circumference of a circle is $14\pi$ . Give the diameter of the circle.

$7\pi$

$8\pi$

Explanation

The circumference can be calculated as $Circumference =2\pi r=\pi d$ , where is the radius of the circle and is the diameter of the circle.

$Circumference =\pi d=14 \pi\Rightarrow d=\frac{14\pi}{\pi}=14$

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be $169 \pi m^2$ .

What is the diameter of the crater?

Explanation

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be $169 \pi m^2$ .